Grade 7 · Expressions & Equations · MAT-07-EE-003
Factor Linear Expressions
Represent and solve factor linear expressions problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve factor linear expressions problems using precise mathematical notation, models, and reasoning.
- Explain why a method for factor linear expressions works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Factor Linear Expressions uses symbols to describe relationships. Equality and inequality are relationships that must be preserved on both sides.
Represent the relationship
The Math Box uses algebra tiles to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify algebra by substituting the proposed solution into the original statement; equivalent expressions must agree for the same input.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Algebra Tiles Lab
Model a linear expression with x-tiles and unit tiles, then evaluate it.
- Model one example of factor linear expressions in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
Factor 4x + 8.
2(2x + 4)Factor out the greatest common factor.
Factor 9x + 15.
3(3x + 5)Factor out the greatest common factor.
Factor 16x + 24.
4(4x + 6)Factor out the greatest common factor.
Factor 25x + 35.
5(5x + 7)Factor out the greatest common factor.
Factor 36x + 48.
6(6x + 8)Factor out the greatest common factor.
Factor 49x + 63.
7(7x + 9)Factor out the greatest common factor.
Factor 16x + 24.
8(2x + 3)Factor out the greatest common factor.
Factor 6x + 8.
2(3x + 4)Factor out the greatest common factor.
Factor 12x + 15.
3(4x + 5)Factor out the greatest common factor.
Factor 20x + 24.
4(5x + 6)Factor out the greatest common factor.
Factor 30x + 35.
5(6x + 7)Factor out the greatest common factor.
Factor 42x + 48.
6(7x + 8)Factor out the greatest common factor.
Factor 14x + 63.
7(2x + 9)Factor out the greatest common factor.
Factor 24x + 24.
8(3x + 3)Factor out the greatest common factor.
Factor 8x + 8.
2(4x + 4)Factor out the greatest common factor.
Factor 15x + 15.
3(5x + 5)Factor out the greatest common factor.
Factor 24x + 24.
4(6x + 6)Factor out the greatest common factor.
Factor 35x + 35.
5(7x + 7)Factor out the greatest common factor.
Factor 12x + 48.
6(2x + 8)Factor out the greatest common factor.
Factor 21x + 63.
7(3x + 9)Factor out the greatest common factor.
Practice
Guided practice with hints
01Factor 32x + 24.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 8(4x + 3)
02Factor 10x + 8.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 2(5x + 4)
03Factor 18x + 15.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 3(6x + 5)
04Factor 28x + 24.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 4(7x + 6)
05Factor 10x + 35.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 5(2x + 7)
06Factor 18x + 48.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 6(3x + 8)
Practice
Independent practice
01Factor 28x + 63.
Answer: 7(4x + 9)
02Factor 40x + 24.
Answer: 8(5x + 3)
03Factor 12x + 8.
Answer: 2(6x + 4)
04Factor 21x + 15.
Answer: 3(7x + 5)
05Factor 8x + 24.
Answer: 4(2x + 6)
06Factor 15x + 35.
Answer: 5(3x + 7)
07Factor 24x + 48.
Answer: 6(4x + 8)
08Factor 35x + 63.
Answer: 7(5x + 9)
Common mistakes
Learn to catch the error, not just the answer.
Use equivalent operations on both sides.
Only terms with the same variable part are like terms.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Translate cost, distance, rate, and measurement situations into symbolic rules.
- Use equations and inequalities to determine unknown quantities, thresholds, and feasible ranges.
Challenge problems
Factor 48x + 24.
8(6x + 3)
Factor 14x + 8.
2(7x + 4)
Factor 6x + 15.
3(2x + 5)
Factor 12x + 24.
4(3x + 6)
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve factor linear expressions problems accurately and justify each result with a valid check.
Practice
Mastery check
01Factor 20x + 35.
Answer: 5(4x + 7)
02Factor 30x + 48.
Answer: 6(5x + 8)
03Factor 42x + 63.
Answer: 7(6x + 9)
04Factor 56x + 24.
Answer: 8(7x + 3)
05Factor 4x + 8.
Answer: 2(2x + 4)
06Factor 9x + 15.
Answer: 3(3x + 5)
07Factor 16x + 24.
Answer: 4(4x + 6)
08Factor 25x + 35.
Answer: 5(5x + 7)
Terminology
Words to know
- variable
- A symbol representing a number that may vary or be unknown.
- coefficient
- A numerical factor multiplying a variable.
- expression
- A combination of numbers, variables, and operations.
- solution
- A value that makes an equation or inequality true.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.